[time-nuts] Re: Build a 3 hat timestanp counter

[Magnus Danielson]

Hi,

The first limit you run into is the 1/tau slope of the measurement 
setup. This is often claimed to be white phase modulation noise, but it 
is also the effect of the single-shot resolution of the counter, and the 
actual slope level depends on the interaction of these two.

So, you might want to try a simple approach first, just to get started. 
Nothing wrong with that. You will end up want to get better, so I will 
try to provide a few guiding comments for things to think of and improve.

So, in general, try to use as high frequency as you can so that as you 
average down, your sqrt(f/f0) gets as high as possible as the benefit 
will be 1/sqrt(f/f0) where f is the oscillator frequency and f0 is the 
rate after average.

As you do ADEV, the f0 frequency will control your bandwidth.

The filter effect of the averaging as you reduce and sub-sample will 
help to some degree with anti-aliasing, but rather than doing averaging, 
consider doing proper anti-aliasing filtering as the effect of aliasing 
into these measures is established and improvements into the upcoming 
IEEE Std 1139 reflect this. In short, aliasing folds the white noise and 
straight averaging tends to be a poor suppressor of aliasing noise.

For white phase modulation (WPM) the expected ADEV response depends 
linearly with the bandwidth of the measurement filter. It's often 
modelled as a brick-wall filter, which it never is. For classical 
counters, the input bandwidth is high, then the sampling rate forms a 
Nyquist sampling frequency, but wide band noise just aliase around that. 
Anti-aliasing filter helps to reduce or even remove the effect, and then 
the bandwidth of the anti-aliasing filter replace the physical channel 
bandwidth. If the anti-aliasing is done digitally after the counter 
front-end, you already got some aliasing wrapping, but keeping that rate 
as high as possible keep the number of overlays low and then 
filtering-wise reduce it will get you better result.

For aliassing effects, see Claudio Calosso of INRIM. Great guy.

This is where the sub-sampling filter approach is nice, since a filter 
followed by sub-sampling removes the need to produce all the outputs of 
the original sample rate, so filter processing can operate on the 
sub-sampled rate.

As your measures goes for higher taus in ADEV, the significant amount of 
the ADEV power will be well within the pass-band of the filter, so just 
making sure you have a flat top avoids surprises. For shorter taus, the 
anti-aliasing filter will be dominant, so assume first decade of tau to 
be waste.

I say this to guide you to get the best result with the proposed setup.

The classical three-cornered hat calculation has a limitation in that it 
becomes limited by noise and can sometimes result in non-stable results. 
The Grosslambert analysis is more robust, since it is essentially the 
same as doing the cross-correlation measurement. The key is that you 
average down before squaring where as in the three-cornered hat to 
square early and is unable to surpress noise of the other sources with 
as good quality. For Grosslambert analysis, see François Vernotte series 
of papers and presentation. François is another great guy. I spent some 
time discussing the Grosslambert analysis with Demetrios the other week. 
I think I need to also say that Demetrios is a great guy too, not to 
single him out, but he really is.

There is another trick up the sleeve thought. If you do the modified 
Allan deviation (MDEV) processing, it actually integrate the sqrt() 
trick with measurement, achieving a 1/tau^1.5 slope for the WPM. This 
will push it down quicker if you let it use enough high rate of samples, 
so that you hit the flicker phase-modulation slope (1/tau), the white 
frequency modulation slope (1/tau^0.5) and finally flicker frequency 
modulation (flat) quicker. The reference levels will be different from 
ADEV for the various noise-types, but that you can look up in tables and 
correct for.

Cheers,
Magnus

On 2022-05-24 18:37, Hans-Georg Lehnard via time-nuts wrote:
> Hi,
>
> my Name is Hans-Georg Lehnard from Germany and I'm new here, worked as a
> developer for hardware then for software and last as a system developer.
> Now I'm retired and I can play with hardware again ;-).
>
> I have:
>
> 4 x 20MHz Rubium (TEMEX MCFRS-1),
> 2 x 10MHz HP10811-60111
> 1 x Samsung UCCM GPSDO
> 1 x FA2 counter.
> lots of OCXO
>
> and try to build a house standard that I can trust and qualify my
> oscillators.
> Reproducible measurements with the FA2 in 10s precision mode I trust to
> 10E-11.
> The short-term stability of the HP oscillators cannot be measured with
> it, or both are defective.
> The FA2 is not suitable for short-term measurements of 0.01 ... 1s.
>
> For measurements against a reference frequency, the stability of the
> reference must be 5 to 10 times better than the measured frequency, and
> I don't have that. Now there are 2 options DMTD mixer or 3-hat
> measurements.
> Because I'm a digital person I chose the 3-hat method.
>
> The idea is now to divide the 3 measuring frequencies (20 or 10 MHz)
> down to 100Khz and to measure the phases with a TDC against the next
> reference edge. Average the measurement results until I am down to 0.001
> ... 1 s. That should improve the 100ps resolution of a TDC7200 far
> enough and can also be output via RS232.
>
> Are my thoughts correct and could it work ?
>
> Hans-Georg
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